Question

The number of arrangements of the letters of the word $BANANA$ in which the two $N$ do not appear adjacently is

• A. $40$
• B. $60$
• C. $80$
• D. $100$

Answer 1

The correct option is A $40$

Total together (string method) of 6 letters (3 A's, 2 N's and 1 B)$=\frac{6!}{2!3!}$

Total together with 3 A's in which 2 N's come together $=\frac{5!}{3!}$

Total in which 2 N's dont come together $=\frac{6!}{2!3!}-\frac{5!}{3!}=40$